ZSPMV (3lapack)

perform the matrix-vector operation y := alpha*A*x + beta*y,

SYNOPSIS

  SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )

      CHARACTER     UPLO

      INTEGER       INCX, INCY, N

      COMPLEX*16    ALPHA, BETA

      COMPLEX*16    AP( * ), X( * ), Y( * )

PURPOSE

  ZSPMV  performs the matrix-vector operation

  where alpha and beta are scalars, x and y are n element vectors and A is an
  n by n symmetric matrix, supplied in packed form.

ARGUMENTS

  UPLO   - CHARACTER*1
         On entry, UPLO specifies whether the upper or lower triangular part
         of the matrix A is supplied in the packed array AP as follows:

         UPLO = 'U' or 'u'   The upper triangular part of A is supplied in
         AP.

         UPLO = 'L' or 'l'   The lower triangular part of A is supplied in
         AP.

         Unchanged on exit.

  N      - INTEGER
         On entry, N specifies the order of the matrix A.  N must be at least
         zero.  Unchanged on exit.

  ALPHA  - COMPLEX*16
         On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

  AP     - COMPLEX*16 array, dimension at least
         ( ( N*( N + 1 ) )/2 ).  Before entry, with UPLO = 'U' or 'u', the
         array AP must contain the upper triangular part of the symmetric
         matrix packed sequentially, column by column, so that AP( 1 )
         contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2,
         2 ) respectively, and so on.  Before entry, with UPLO = 'L' or 'l',
         the array AP must contain the lower triangular part of the symmetric
         matrix packed sequentially, column by column, so that AP( 1 )
         contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3,
         1 ) respectively, and so on.  Unchanged on exit.

  X      - COMPLEX*16 array, dimension at least
         ( 1 + ( N - 1 )*abs( INCX ) ).  Before entry, the incremented array
         X must contain the N- element vector x.  Unchanged on exit.

  INCX   - INTEGER
         On entry, INCX specifies the increment for the elements of X. INCX
         must not be zero.  Unchanged on exit.

  BETA   - COMPLEX*16
         On entry, BETA specifies the scalar beta. When BETA is supplied as
         zero then Y need not be set on input.  Unchanged on exit.

  Y      - COMPLEX*16 array, dimension at least
         ( 1 + ( N - 1 )*abs( INCY ) ).  Before entry, the incremented array
         Y must contain the n element vector y. On exit, Y is overwritten by
         the updated vector y.

  INCY   - INTEGER
         On entry, INCY specifies the increment for the elements of Y. INCY
         must not be zero.  Unchanged on exit.